The present invention relates to a magnetic resonance (MR) imaging system which utilizes the MR phenomenon to noninvasively measure information about the density and relaxation time of a specific nucleus in a given region, for example, a slice, of a body under examination, thereby forming MR images useful for medical diagnosis, and more particularly, to a method and a system for MR imaging which separately provides MR images of water and fat of the body.
According to a typical MR imaging method for obtaining an MR image of hydrogen nuclei, i.e., protons, the complex image of protons in water and the complex image of protons in fat cannot be obtained separately and independently. However, with the use of the so-called chemical shift phenomenon (e.g., the protons in water and the protons in fat resonate at different frequencies, in the same magnetic field), the MR images of water and fat can separately be obtained. This type of imaging method for separating the MR image of water from that of fat is proposed in W. T. Dixon Radiology, page 153, by W. T. Dixon, 1984. A brief explanation of this method will be given below referring to FIG. 1.
As shown in FIG. 1, with a static field applied to a body under examination, a gradient field for slice determination (the static field and gradient field are not illustrated) and a .pi./2 pulse (90.degree. pulse) are applied to the body, and after the elapse of the time (T.sub.E /2)-.DELTA.T from the application of .pi./2 pulse, the gradient field (not shown) for slice determination and a .pi. pulse (180.degree. pulse) are applied to the body. After the elapse of time T.sub.E from the application of the .pi./2 pulse, an MR echo is observed. (A phase encoding gradient field or read gradient field may be used as desired.) In this case, the interval .tau..sub.1 between the .pi./2 pulse and the .pi. pulse is EQU .tau..sub.1 =(T.sub.E /2)-.DELTA.T
where T.sub.E, the echo time, is the interval between the .pi./2 pulse and the MR echo, and the interval .tau..sub.2 between the .pi. pulse and the MR echo is EQU .tau..sub.2 =(T.sub.E /2)+.DELTA.T.
Thus, EQU .tau..sub.2 -.tau..sub.1 =2.DELTA.T.
With the chemical shift in water and fat protons being denoted as .delta., due to the time lag of 2.DELTA.T, the water protons and the fat protons have a phase difference of: EQU .DELTA..psi.=.delta..gamma.Ho(2.DELTA.T) (1)
where .gamma. is a Larmor constant or gyromagnetic ratio, and Ho is a static field intensity.
Now, let .DELTA.T=.pi./(2.delta..gamma.Ho), which yields .DELTA..psi.=.pi., and the phase of water is opposite to the phase of fat. Image data attained at this time, f.pi., is expressed as follows: EQU f.pi.=f.sub.W -f.sub.F ( 2)
where f.sub.W is water distribution information and f.sub.F is fat distribution information.
With image data fo attained in an ordinary imaging or at the time .DELTA.T=0, the water protons are in phase with the fat protons. Thus EQU f.sub.o =f.sub.W +f.sub.F ( 3).
Adding equations (2) and (3) yields f.sub.W =(fo+f.pi.)/2, and subtracting equation (2) from equation (3) yields f.sub.F =(fo-f.pi.)/2.
The above is a summary of the imaging method proposed by W. T. Dixon.
Let us now consider the inhomogeneity of the static field. This inhomogeneity in the MR imaging, which varies depending on the size or state of an image pickup region, is considered to be several ppm or less when a body under examination by a typical system is a human body. This inhomogeneity can be expressed by .DELTA.H that is a function of spatial positions or coordinates (x,y,z). Since the chemical shift .delta. corresponds to about 3.5 ppm, the inhomogeneity .DELTA.H is nearly equal to the chemical shift or greater in some cases. Due to the inhomogeneity of the static field, therefore, an image is distorted. This distortion is called a static field distortion. The image data f.pi.(x,y) actually includes the influence of the inhomogeneity .DELTA.H. This actual image data f.pi.(x,y) that includes the influence of .DELTA.H is expressed as: EQU f.pi.(x,y)=e.sup.i.gamma..DELTA.H(x,y).multidot.2.DELTA.T) (f.sub.W (x,y)-f.sub.F (x,y) (4)
In equation (4), (x,y) means the position of the coordinate system which is properly determined on a plane including the target slice. Since the inhomogeneity .DELTA.H of the static field depends on the spatial positions as mentioned earlier, different influences would appear on a reconstructed image, depending on the pixels. In the Dixon report, the absolute value of a complex number of actual image data f.pi., namely .vertline.f.sub.w -f.sub.F .vertline., is obtained and is used for f.sub.W -f.sub.F. In this case, it is not distinguished whether f.sub.W is greater or smaller than f.sub.F, so that the static field distortion cannot be correctly compensated. This static field distortion .DELTA.H(x,y) may be compensated as follows:
The image of a water phantom is picked up in advance in the sequence with .DELTA.T=.pi./(2.delta..gamma.Ho) as is done to attain f.pi., and its image data is denoted by p.pi.(x,y), which is expressed as follows: EQU p.pi.(x,y)=e.sup.i.gamma..DELTA.H(x,y).multidot.2.DELTA.T) po(x,y) (5)
In equation (5), po(x,y) is the image data of the water phantom when .DELTA.T=0. (As should be clear from equation (4), the image data attained when .DELTA.T=0 is not influenced by the inhomogeneity .DELTA.H of the static field.) And, ##EQU1## As f.pi.(x,y) in equation (6) is equal to f.sub.W (x,y)-f.sub.F (x,y), the static distortion can be compensated.
However, to carry out this compensation, it is necessary to use sufficiently accurate compensating image data p.pi.. Since the calculation using such accurate data is complicated to perform, it requires a very long time. Therefore, the compensation for the field by the above method is not practical.
Neglecting the static field distortion, separate image data of water and fat of a quality suitable for medical diagnosis cannot be attained.